#Magic Initiate: No

Having the Feat 'Magic Initiate' does not grant the character an additional class. Since the rule for spell scrolls is:

> ...if the spell is on your class's list...

The character would still not have the spell in its class list if it did not before the Feat.

Edit: Ritual Caster added

#Ritual Caster: No

A ritual caster can only cast spells from their ritual book. The Spell Scroll can be used to add a new spell to the ritual book, but don't forget more of what Ritual Caster says:

> The spell must be on the spell list for the class you chose, the spell's level can be no higher than half your level (rounded up), and it must have the ritual tag

It seems that the Ritual Caster is a more specific rule than the generic rule about Spell Scrolls, so it follows the player can use the spell scroll to add a new ritual long as you follow all the rules of the Ritual Caster.